A representation theorem for the error of recursive estimators

Gerencsér, László (2006) A representation theorem for the error of recursive estimators. In: CDC 2006. 45th IEEE conference on decision and control. San Diego, 2006..

Full text not available from this repository.

Abstract

The objective of this paper is to present advanced and less known techniques for the analysis of performance degradation due to statistical uncertainty for a wide class of linear stochastic systems in a rigorous and concise manner. The main technical advance of the present paper is a strong approximation theorem for the Djereveckii--Fradkov--Ljung (DFL) scheme with enforced boundedness, in which, for any $q ge 1$, the $L_q$-norms of the so-called residual terms are shown to tend to zero with rate $N^{-1/2-varepsilon}$ with some $varepsilon > 0$. This is a significant extension of previous results for the recursive prediction error or RPE estimator of ARMA processes given in [L.~Gerencs'er, {it Systems Control Lett.}, 21 (1993), pp.~347--351. Two useful corollaries will be presented. In the first a standard transform of the estimation-error process will be shown to be $L$-mixing. In the second the asymptotic covariance matrix of the estimator will be given. An application to the minimum-variance self-tuning regulator for ARMAX systems will be described.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: adaptive prediction, stochastic complexity, recursive estimation, $L$-mixing processes, asymptotic covariance, stochastic adaptive control
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:26
Last Modified: 11 Dec 2012 15:26
URI: http://eprints.sztaki.hu/id/eprint/4503

Update Item Update Item